Introduction and Results

  • Eli Levin
  • Doron S. Lubinsky
Part of the CMS Books in Mathematics book series (CMSBM)

Abstract

Let I be a finite or infinite interval and let w: I → [0, ∞) be measurable with all power moments
$$ \int_{I} {{x^{n}}w(x)dx,{\text{ n = 0, 1, 2, 3,}}...} "$$
finite. Then we call w a weight and may define orthonormal polynomials
$$ {p_{n}}(x) = {p_{n}}(w,{\text{ }}x) = {\gamma _{n}}(w){x^{n}} + \cdot \cdot \cdot ,{\gamma _{n}}(w) > 0, "$$
satisfying
$$ \int_{I} {{p_{n}}{p_{m}}w = {d_{{mn}}},m, n = 0, 1, 2,... .} "$$

Keywords

Stein cosB 

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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Eli Levin
    • 1
  • Doron S. Lubinsky
    • 2
  1. 1.Department of MathematicsThe Open University of IsraelTel AvivIsrael
  2. 2.Centre for Applicable Analysis and Number Theory Department of MathematicsWitwatersrand UniversityWitsSouth Africa

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